{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MKGOMKKKBK2BCARJUVSZVCRTSQ","short_pith_number":"pith:MKGOMKKK","canonical_record":{"source":{"id":"1501.05020","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-20T23:33:56Z","cross_cats_sorted":["cs.CG","cs.DM"],"title_canon_sha256":"b52258d9cdbbc6b3a744149518e15e28da58e533237fad884b1d37788523be06","abstract_canon_sha256":"61eb24df3d02b1eafea0dcecf4b7ce7d58bc194b3049573a31084aaf8a044514"},"schema_version":"1.0"},"canonical_sha256":"628ce6294a0ab4110229a5659a8a3394163d0326c430a65f12ee49ba6aa08e97","source":{"kind":"arxiv","id":"1501.05020","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05020","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05020v3","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05020","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"MKGOMKKKBK2B","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MKGOMKKKBK2BCARJ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MKGOMKKK","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MKGOMKKKBK2BCARJUVSZVCRTSQ","target":"record","payload":{"canonical_record":{"source":{"id":"1501.05020","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-20T23:33:56Z","cross_cats_sorted":["cs.CG","cs.DM"],"title_canon_sha256":"b52258d9cdbbc6b3a744149518e15e28da58e533237fad884b1d37788523be06","abstract_canon_sha256":"61eb24df3d02b1eafea0dcecf4b7ce7d58bc194b3049573a31084aaf8a044514"},"schema_version":"1.0"},"canonical_sha256":"628ce6294a0ab4110229a5659a8a3394163d0326c430a65f12ee49ba6aa08e97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:13.575077Z","signature_b64":"Xh3xzVxIH9ergFiUf+GnyIMZ4fhLiH6/Xg9c9GvwhW7hFUoGRqPkDKFbIqxVfcZwyh5K9TgMOvZwOZ3s0ENIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"628ce6294a0ab4110229a5659a8a3394163d0326c430a65f12ee49ba6aa08e97","last_reissued_at":"2026-05-18T01:21:13.574577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:13.574577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.05020","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WFiQiVoLuaDn6qgcFkHw/et35YPhc1nzJu9zfaSnWhNn8GGtFMDn9R/knKbmn9s7S7mnsEXmmKx1TgrgLxaDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:43:01.315115Z"},"content_sha256":"0bfef8ec65e26465defeec4a89547810aee2ef56c63b787fac40695fed28556c","schema_version":"1.0","event_id":"sha256:0bfef8ec65e26465defeec4a89547810aee2ef56c63b787fac40695fed28556c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MKGOMKKKBK2BCARJUVSZVCRTSQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Layouts of Expander Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DM"],"primary_cat":"math.CO","authors_text":"Anastasios Sidiropoulos, David R. Wood, Vida Dujmovi\\'c","submitted_at":"2015-01-20T23:33:56Z","abstract_excerpt":"Bourgain and Yehudayoff recently constructed $O(1)$-monotone bipartite expanders. By combining this result with a generalisation of the unraveling method of Kannan, we construct 3-monotone bipartite expanders, which is best possible. We then show that the same graphs admit 3-page book embeddings, 2-queue layouts, 4-track layouts, and have simple thickness 2. All these results are best possible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05020","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GP4gnkk8bC31UweAkRw+5ZgWEz+yo4hQ9r6q4Z0ODRnl/vOVm4wtdSFTOPmYOcFw2fv5prjvFors1LG/EWZTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:43:01.315845Z"},"content_sha256":"fa4277fd80e68d34ef73109e42319e17d1eb897e5f985cd9f4500b61800d5c0f","schema_version":"1.0","event_id":"sha256:fa4277fd80e68d34ef73109e42319e17d1eb897e5f985cd9f4500b61800d5c0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MKGOMKKKBK2BCARJUVSZVCRTSQ/bundle.json","state_url":"https://pith.science/pith/MKGOMKKKBK2BCARJUVSZVCRTSQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MKGOMKKKBK2BCARJUVSZVCRTSQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T23:43:01Z","links":{"resolver":"https://pith.science/pith/MKGOMKKKBK2BCARJUVSZVCRTSQ","bundle":"https://pith.science/pith/MKGOMKKKBK2BCARJUVSZVCRTSQ/bundle.json","state":"https://pith.science/pith/MKGOMKKKBK2BCARJUVSZVCRTSQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MKGOMKKKBK2BCARJUVSZVCRTSQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MKGOMKKKBK2BCARJUVSZVCRTSQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"61eb24df3d02b1eafea0dcecf4b7ce7d58bc194b3049573a31084aaf8a044514","cross_cats_sorted":["cs.CG","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-20T23:33:56Z","title_canon_sha256":"b52258d9cdbbc6b3a744149518e15e28da58e533237fad884b1d37788523be06"},"schema_version":"1.0","source":{"id":"1501.05020","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05020","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05020v3","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05020","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"MKGOMKKKBK2B","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MKGOMKKKBK2BCARJ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MKGOMKKK","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:fa4277fd80e68d34ef73109e42319e17d1eb897e5f985cd9f4500b61800d5c0f","target":"graph","created_at":"2026-05-18T01:21:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Bourgain and Yehudayoff recently constructed $O(1)$-monotone bipartite expanders. By combining this result with a generalisation of the unraveling method of Kannan, we construct 3-monotone bipartite expanders, which is best possible. We then show that the same graphs admit 3-page book embeddings, 2-queue layouts, 4-track layouts, and have simple thickness 2. All these results are best possible.","authors_text":"Anastasios Sidiropoulos, David R. Wood, Vida Dujmovi\\'c","cross_cats":["cs.CG","cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-20T23:33:56Z","title":"Layouts of Expander Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05020","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0bfef8ec65e26465defeec4a89547810aee2ef56c63b787fac40695fed28556c","target":"record","created_at":"2026-05-18T01:21:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"61eb24df3d02b1eafea0dcecf4b7ce7d58bc194b3049573a31084aaf8a044514","cross_cats_sorted":["cs.CG","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-20T23:33:56Z","title_canon_sha256":"b52258d9cdbbc6b3a744149518e15e28da58e533237fad884b1d37788523be06"},"schema_version":"1.0","source":{"id":"1501.05020","kind":"arxiv","version":3}},"canonical_sha256":"628ce6294a0ab4110229a5659a8a3394163d0326c430a65f12ee49ba6aa08e97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"628ce6294a0ab4110229a5659a8a3394163d0326c430a65f12ee49ba6aa08e97","first_computed_at":"2026-05-18T01:21:13.574577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:13.574577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xh3xzVxIH9ergFiUf+GnyIMZ4fhLiH6/Xg9c9GvwhW7hFUoGRqPkDKFbIqxVfcZwyh5K9TgMOvZwOZ3s0ENIDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:13.575077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05020","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bfef8ec65e26465defeec4a89547810aee2ef56c63b787fac40695fed28556c","sha256:fa4277fd80e68d34ef73109e42319e17d1eb897e5f985cd9f4500b61800d5c0f"],"state_sha256":"f7df9c2f09c3704bd36eddcaf7fd8554c9112633ef4db2cbdf9855d179aeabdd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hyoweeSpUBEz8/vgvQ2RRJc7wr6gd4yowQBIDfmdRcDVOPQXP8R6twqWi86bQK6CTtQ+oa3tcdAK4Wy04BWsAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:43:01.319182Z","bundle_sha256":"06077eacc8228191e5e42311d6902f82c791b09ea6ce1d360e2cdb7394c519ae"}}